This is nth to do with her family background, is her personality. Some ppl are like that, i think she is afriad that your mum will dote you more. But, which parents dont dote their own daughter more? Just let her sabo, the more she wants to sabo you, the easier she will show her bad personality to your family.
I dont see any pro buying a property to invest or even stay in it. Is your sister In law going to shift into your parents' place after married? if so, i think she will spout more nonsense. Tell your parents to trust you, dont listen to an outsider and come and confront you. They have been trusting you for so many yrs, dont spoil the r/s just becos of your sister In law.
Since she is such person, like to badmouth ppl, I'm sure she will do it again and again, cos I encounter such friends before, true, at 1st ppl will believe them but after sometime ppl will slowly think back "how come she can badmouth on EVERYONE?" I'm sure your parents will 'wake up' one day. You dont badmouth her though she badmouth you, let her be and i'm sure one day she will either stop it (cos no one entertains her) or continue to badmouth ppl until everyone loathes her. =)